def test_4(self, presets_load_coefficientfunction_into_gridfunction):
""" Check that the coefficientfunction and gridfunction dimensions must agree. Check 2D and 3D. """
mesh_2d, fes_scalar_2d, fes_vector_2d, fes_mixed_2d, mesh_3d, fes_scalar_3d, fes_vector_3d, fes_mixed_3d = presets_load_coefficientfunction_into_gridfunction
cfu_scalar = ngs.CoefficientFunction(ngs.x + ngs.y)
gfu_mixed_2d = ngs.GridFunction(fes_mixed_2d)
cfu_vector_2d = ngs.CoefficientFunction((ngs.x, ngs.y))
gfu_mixed_3d = ngs.GridFunction(fes_mixed_3d)
cfu_vector_3d = ngs.CoefficientFunction((ngs.x, ngs.y, ngs.z))
# Check 2D.
with pytest.raises(netgen.libngpy._meshing.NgException):
coef_dict = {1: cfu_vector_2d} # Vector coefficientfunction but scalar gridfunction.
load_coefficientfunction_into_gridfunction(gfu_mixed_2d, coef_dict)
with pytest.raises(netgen.libngpy._meshing.NgException):
coef_dict = {0: cfu_scalar} # Scalar coefficientfunction but vector gridfunction.
load_coefficientfunction_into_gridfunction(gfu_mixed_2d, coef_dict)
# Check 3D.
with pytest.raises(netgen.libngpy._meshing.NgException):
coef_dict = {1: cfu_vector_3d} # Vector coefficientfunction but scalar gridfunction.
load_coefficientfunction_into_gridfunction(gfu_mixed_3d, coef_dict)
with pytest.raises(netgen.libngpy._meshing.NgException):
coef_dict = {0: cfu_scalar} # Scalar coefficientfunction but vector gridfunction.
load_coefficientfunction_into_gridfunction(gfu_mixed_3d, coef_dict)
def test_2(self, presets_load_coefficientfunction_into_gridfunction):
"""
Check that coefficientfunctions can be loaded into different component of a gridfunction correctly. Check 2D and
3D. Also check scalar and vector coefficientfunctions.
"""
mesh_2d, fes_scalar_2d, fes_vector_2d, fes_mixed_2d, mesh_3d, fes_scalar_3d, fes_vector_3d, fes_mixed_3d = presets_load_coefficientfunction_into_gridfunction
cfu_scalar = ngs.CoefficientFunction(ngs.x + ngs.y)
gfu_mixed_2d = ngs.GridFunction(fes_mixed_2d)
cfu_vector_2d = ngs.CoefficientFunction((ngs.x, ngs.y))
coef_dict_2d = {0: cfu_vector_2d, 1: cfu_scalar}
gfu_mixed_3d = ngs.GridFunction(fes_mixed_3d)
cfu_vector_3d = ngs.CoefficientFunction((ngs.x, ngs.y, ngs.z))
coef_dict_3d = {0: cfu_vector_3d, 1: cfu_scalar}
# Check 2D
load_coefficientfunction_into_gridfunction(gfu_mixed_2d, coef_dict_2d)
err_scalar_2d = ngs.Integrate((cfu_scalar - gfu_mixed_2d.components[1]) * (cfu_scalar - gfu_mixed_2d.components[1]), mesh_2d)
err_vector_2d = ngs.Integrate((cfu_vector_2d - gfu_mixed_2d.components[0]) * (cfu_vector_2d - gfu_mixed_2d.components[0]), mesh_2d)
assert math.isclose(err_scalar_2d, 0.0, abs_tol=1e-16)
assert math.isclose(err_vector_2d, 0.0, abs_tol=1e-16)
# Check 3D
load_coefficientfunction_into_gridfunction(gfu_mixed_3d, coef_dict_3d)
err_scalar_3d = ngs.Integrate((cfu_scalar - gfu_mixed_3d.components[1]) * (cfu_scalar - gfu_mixed_3d.components[1]), mesh_3d)
err_vector_3d = ngs.Integrate((cfu_vector_3d - gfu_mixed_3d.components[0]) * (cfu_vector_3d - gfu_mixed_3d.components[0]), mesh_3d)
assert math.isclose(err_scalar_3d, 0.0, abs_tol=1e-16)
assert math.isclose(err_vector_3d, 0.0, abs_tol=1e-16)
def getPair(self, fes, s):
xr, xi = self.A.createVecs()
lam = self.E.getEigenpair(s, xr, xi)
vecmap = VectorMapping(fes.ParallelDofs(), fes.FreeDofs())
vr = ngs.GridFunction(fes)
vecmap.P2N(xr, vr.vec)
vi = ngs.GridFunction(fes)
vecmap.P2N(xi, vi.vec)
return lam, vr, vi
def getPairs(self, fes):
vr = ngs.GridFunction(fes, multidim=self.N)
vi = ngs.GridFunction(fes, multidim=self.N)
lam = []
for s in range(self.N):
xr, xi = self.A.createVecs()
lam.append(self.E.getEigenpair(s, xr, xi))
vecmap = VectorMapping(fes.ParallelDofs(), fes.FreeDofs())
vecmap.P2N(xr, vr.vecs[s])
vecmap.P2N(xi, vi.vecs[s])
return lam, vr, vi
def __init__(self, domain, form):
assert isinstance(domain, NgsSpace)
if isinstance(form, ngs.BilinearForm):
assert domain.fes == form.space
form.Assemble()
mat = form.mat
elif isinstance(form, ngs.BaseMatrix):
mat = form
else:
raise TypeError('Invalid type: {}'.format(type(form)))
self.mat = mat
"""The assembled matrix."""
super().__init__(domain, domain, linear=True)
self._gfu_in = ngs.GridFunction(domain.fes)
self._gfu_out = ngs.GridFunction(domain.fes)
self._inverse = None
def Solve(a, f, c, ms=100, tol=1e-12, nocb=True):
ngs.ngsglobals.msg_level = 5
gfu = ngs.GridFunction(a.space)
with ngs.TaskManager():
a.Assemble()
f.Assemble()
ngs.ngsglobals.msg_level = 1
c.Test()
cb = None if a.space.mesh.comm.rank != 0 or nocb else lambda k, x: print(
"it =", k, ", err =", x)
cg = ngs.krylovspace.CGSolver(mat=a.mat,
pre=c,
callback=cb,
maxsteps=ms,
tol=tol)
ngs.mpi_world.Barrier()
ts = ngs.mpi_world.WTime()
cg.Solve(sol=gfu.vec, rhs=f.vec)
ngs.mpi_world.Barrier()
ts = ngs.mpi_world.WTime() - ts
if ngs.mpi_world.rank == 0:
print("---")
print("multi-dim ", a.space.dim)
print("(vectorial) ndof ", a.space.ndofglobal)
print("(scalar) ndof ", a.space.dim * a.space.ndofglobal)
print("used nits = ", cg.iterations)
print("(vec) dofs / (sec * np) = ",
a.space.ndofglobal / (ts * max(ngs.mpi_world.size - 1, 1)))
print("(scal) dofs / (sec * np) = ",
(a.space.ndofglobal * a.space.dim) /
(ts * max(ngs.mpi_world.size - 1, 1)))
print("---")
assert cg.errors[-1] < tol * cg.errors[0]
assert cg.iterations < ms
return gfu
def test_h1_real():
"""Test h1 amg for real example."""
with ngs.TaskManager():
mesh = ngs.Mesh(unit_square.GenerateMesh(maxh=0.2))
fes = ngs.H1(mesh, dirichlet=[1, 2, 3], order=1)
u = fes.TrialFunction()
v = fes.TestFunction()
# rhs
f = ngs.LinearForm(fes)
f += ngs.SymbolicLFI(v)
f.Assemble()
# lhs
a = ngs.BilinearForm(fes, symmetric=True)
a += ngs.SymbolicBFI(grad(u) * grad(v))
c = ngs.Preconditioner(a, 'h1amg2')
a.Assemble()
solver = ngs.CGSolver(mat=a.mat, pre=c.mat)
gfu = ngs.GridFunction(fes)
gfu.vec.data = solver * f.vec
assert_greater(solver.GetSteps(), 0)
assert_less_equal(solver.GetSteps(), 4)
def test_parallel():
mesh = ngs.Mesh(unit_square.GenerateMesh(maxh=0.2))
fes = ngs.L2(mesh, order=5, complex=True)
g1 = ngs.GridFunction(fes)
g2 = ngs.GridFunction(fes)
for order in range(10):
functions = [(f(ngs.x + 1j * ngs.y, order)) for f in fs_ng]
for f in functions:
g1.Set(f)
with ngs.TaskManager():
g2.Set(f)
error = ngs.Integrate(g1 - g2, mesh)
assert error == 0j
def load_bc_gridfunctions(self, bc_dict: Dict, fes: ngs.FESpace,
model_components: Dict[str, int]) -> Dict:
"""
Function to load any saved gridfunctions that should be used to specify BCs.
Args:
bc_dict: Dict specifying the BCs and their mesh markers for each variable.
fes: The finite element space of the model.
model_components: Maps between variable names and their component in the finite element space.
Returns:
bc_dict: The same dict now, where appropriate, holding gridfunctions in place of strings holding the paths
to those gridfunctions
"""
for bc_type in bc_dict.keys():
for var in bc_dict[bc_type].keys():
if var in ['u', 'p']:
component = model_components[var]
else:
# For things like stress, no_backflow, all...
component = None
for marker, val in bc_dict[bc_type][var].items():
if isinstance(val, str):
# Need to load a gridfunction from file.
# Check that the file exists.
val = self._find_rel_path_for_file(val)
if component is None:
# Use the full finite element space.
gfu_val = ngs.GridFunction(fes)
gfu_val.Load(val)
else:
# Use a component of the finite element space.
gfu_val = ngs.GridFunction(
fes.components[component])
gfu_val.Load(val)
# Replace the value in the BC dictionary.
bc_dict[bc_type][var][marker] = gfu_val
else:
# Already parsed
pass
return bc_dict
def test_1(self, presets_load_coefficientfunction_into_gridfunction):
""" Check that a coefficientfunction can be loaded into a full gridfunction correctly. Check 2D and 3D. """
mesh_2d, fes_scalar_2d, fes_vector_2d, fes_mixed_2d, mesh_3d, fes_scalar_3d, fes_vector_3d, fes_mixed_3d = presets_load_coefficientfunction_into_gridfunction
gfu_scalar_2d = ngs.GridFunction(fes_scalar_2d)
gfu_scalar_3d = ngs.GridFunction(fes_scalar_3d)
cfu_scalar = ngs.CoefficientFunction(ngs.x + ngs.y)
coef_dict = {None: cfu_scalar}
# Check 2D
load_coefficientfunction_into_gridfunction(gfu_scalar_2d, coef_dict)
err_2d = ngs.Integrate((cfu_scalar - gfu_scalar_2d) * (cfu_scalar - gfu_scalar_2d), mesh_2d)
assert math.isclose(err_2d, 0.0, abs_tol=1e-16)
# Check 3D
load_coefficientfunction_into_gridfunction(gfu_scalar_3d, coef_dict)
err_3d = ngs.Integrate((cfu_scalar - gfu_scalar_3d) * (cfu_scalar - gfu_scalar_3d), mesh_3d)
assert math.isclose(err_3d, 0.0, abs_tol=1e-16)
def _l_inf(sol: GridFunction, ref_sol: Union[GridFunction,
CoefficientFunction], mesh: Mesh,
fes: FESpace) -> float:
""" L-infinity norm """
gfu_tmp = ngs.GridFunction(fes)
gfu_tmp.Set(sol - ref_sol)
# NGSolve has no builtin method for evalutating the L-infinity norm and recommends using numpy
arr = gfu_tmp.vec.FV().NumPy()
return np.max(np.abs(arr))
def construct_gfu(self) -> ngs.GridFunction:
"""
Function to construct a solution GridFunction.
Returns:
~: A GridFunction initialized on the finite element space of the model
"""
gfu = ngs.GridFunction(self.fes)
return gfu
def test_3(self, presets_load_coefficientfunction_into_gridfunction):
""" Check that passing in a coef_dict with multiple keys, one of which is None raises an error. """
mesh_2d, fes_scalar_2d, fes_vector_2d, fes_mixed_2d, mesh_3d, fes_scalar_3d, fes_vector_3d, fes_mixed_3d = presets_load_coefficientfunction_into_gridfunction
gfu = ngs.GridFunction(fes_scalar_2d)
cfu_1 = ngs.CoefficientFunction(ngs.x + ngs.y)
cfu_2 = ngs.CoefficientFunction(ngs.x * ngs.y)
coef_dict = {None: cfu_1, 0: cfu_2}
with pytest.raises(AssertionError):
load_coefficientfunction_into_gridfunction(gfu, coef_dict)
def inital_span(X):
# Coefficient funtions in the span.
coeffs = (ng.CoefficientFunction([1]), ng.x, ng.y)
# The span as a list.
span = [ng.GridFunction(X) for k in range(len(coeffs))]
# Set the values of each GridFunction.
for k in range(len(coeffs)):
span[k].Set(coeffs[k])
return span
def rbms(dim, V, rots):
if rots:
tups = [(1, 0, 0), (0, 1, 0), (y, -x, 1)]
else:
tups = [(1, 0), (0, 1), (y, -x)]
cfs = [ngsolve.CoefficientFunction(x) for x in tups]
gf = ngsolve.GridFunction(V)
kvecs = [gf.vec.CreateVector() for c in cfs]
for vec, cf in zip(kvecs, cfs):
gf.Set(cf)
vec.data = gf.vec
return kvecs
def GetData(self, set_minmax=True):
import json
d = BuildRenderData(self.mesh, self.cf, self.order, draw_surf=self.draw_surf, draw_vol=self.draw_vol, deformation=self.deformation)
if isinstance(self.cf, ngs.GridFunction) and len(self.cf.vecs)>1:
# multidim gridfunction - generate data for each component
gf = ngs.GridFunction(self.cf.space)
dim = len(self.cf.vecs)
data = []
for i in range(1,dim):
gf.vec.data = self.cf.vecs[i]
data.append(BuildRenderData(self.mesh, gf, self.order, draw_surf=self.draw_surf, draw_vol=self.draw_vol, deformation=self.deformation))
d['multidim_data'] = data
d['multidim_interpolate'] = self.interpolate_multidim
d['multidim_animate'] = self.animate
if set_minmax:
if self.min is not None:
d['funcmin'] = self.min
if self.max is not None:
d['funcmax'] = self.max
d['autoscale'] = self.autoscale
if self.clipping is not None:
d['clipping'] = True
if isinstance(self.clipping, dict):
allowed_args = ("x", "y", "z", "dist", "function", "pnt", "vec")
if "vec" in self.clipping:
vec = self.clipping["vec"]
self.clipping["x"] = vec[0]
self.clipping["y"] = vec[1]
self.clipping["z"] = vec[2]
if "pnt" in self.clipping:
d['mesh_center'] = list(self.clipping["pnt"])
for name, val in self.clipping.items():
if not (name in allowed_args):
raise Exception('Only {} allowed as arguments for clipping!'.format(", ".join(allowed_args)))
d['clipping_' + name] = val
if self.vectors is not None:
d['vectors'] = True
if isinstance(self.vectors, dict):
for name, val in self.vectors.items():
if not (name in ("grid_size", "offset")):
raise Exception('Only "grid_size" and "offset" allowed as arguments for vectors!')
d['vectors_' + name] = val
return d
def mean_to_zero(gfu: GridFunction, fes: FESpace, mesh: Mesh) -> GridFunction:
"""
Function to bias a gridfunction so its mean is zero.
Args:
gfu: The gridfunction to modify (or a component of a gridfunction).
fes: The finite element space the gridfunction is defined on.
mesh: The mesh the gridfunction is defined on.
Returns:
gfu_biased: The modified gridfunction.
"""
avg = mean(gfu, mesh)
gfu_biased = ngs.GridFunction(fes)
gfu_biased.Set(gfu - avg)
return gfu_biased
def linear_combo(v, W):
"""
Method that multiplies the list v containing the span of our vectors
to the matrix W that solved the eigenproblem
vAv*W = vBv*W*E,
where E is the diagonal matrix of eigenvalues.
"""
# Create an array of new eigenfunctions.
q = []
for k in range(len(v)):
q += [ng.GridFunction(v[k].space)]
q[k].Set(ng.CoefficientFunction(0))
# Now set the values of each new grid function.
for k in range(len(q)):
for m in range(len(v)):
q[k].vec.data += np.complex(W[m, k]) * v[m].vec
return q
def GetData(self, set_minmax=True):
import json
d = BuildRenderData(self.mesh,
self.cf,
self.order,
draw_surf=self.draw_surf,
draw_vol=self.draw_vol,
deformation=self.deformation)
if isinstance(self.cf, ngs.GridFunction) and len(self.cf.vecs) > 1:
# multidim gridfunction - generate data for each component
gf = ngs.GridFunction(self.cf.space)
dim = len(self.cf.vecs)
data = []
for i in range(1, dim):
gf.vec.data = self.cf.vecs[i]
data.append(
BuildRenderData(self.mesh,
gf,
self.order,
draw_surf=self.draw_surf,
draw_vol=self.draw_vol,
deformation=self.deformation))
d['multidim_data'] = data
d['multidim_interpolate'] = self.interpolate_multidim
d['multidim_animate'] = self.animate
if set_minmax:
if self.min is not None:
d['funcmin'] = self.min
if self.max is not None:
d['funcmax'] = self.max
d['autoscale'] = self.autoscale
return d
def apply_spectral_projector(ng_comm, X, zbas, precs, Bq, w, P_q0):
# Create a scratch grid function for this computation.
tmp = ng.GridFunction(X)
for k in range(len(zbas)):
for m in range(len(Bq)):
tmp.Set(0.0 + 0.0j)
# Run the conjugate gradient method. This step computes the
# solution w = (zB - A)^{-1} B*f[m] for each of the m
# right-hand-sides f[m].
MyGMRes(A=zbas[k].mat,
b=Bq[m],
pre=precs[k],
freedofs=None,
x=tmp.vec,
maxsteps=2000,
tol=1e-14,
innerproduct=None,
restart=None,
printrates=False)
P_q0[m].vec.data += np.complex(w[k]) * tmp.vec
def poisson_solve():
fes = H1(mesh, order=3, dirichlet="left|right|bottom|top")
u = fes.TrialFunction()
v = fes.TestFunction()
f = LinearForm(fes)
f += -((4 * x**2 - 2) * ng.exp(-x**2) +
(4 * y**2 - 2) * ng.exp(-y**2)) * v * dx
a = BilinearForm(fes)
a += grad(u) * grad(v) * dx
a.Assemble()
f.Assemble()
uₕ = ng.GridFunction(fes)
uₕ.Set(uexact, ng.BND)
α = f.vec.CreateVector()
α.data = f.vec - a.mat * uₕ.vec
uₕ.vec.data += a.mat.Inverse(freedofs=fes.FreeDofs()) * α
return uₕ
fes = ngs.H1(mesh, dirichlet=[1, 2, 3], order=1)
u = fes.TrialFunction()
v = fes.TestFunction()
# rhs
f = ngs.LinearForm(fes)
f += ngs.SymbolicLFI(v)
# lhs
a = ngs.BilinearForm(fes, symmetric=True)
a += ngs.SymbolicBFI(grad(u) * grad(v))
c = ngs.Preconditioner(a, 'h1amg', test=True)
gfu = ngs.GridFunction(fes)
bvp = ngs.BVP(bf=a, lf=f, gf=gfu, pre=c)
while True:
fes.Update()
gfu.Update()
a.Assemble()
f.Assemble()
bvp.Do()
ngs.Draw(gfu, mesh, 'solution')
input('Hit enter for refinement')
mesh.Refine()
codomain = NgsSpace(fes_codomain)
rhs = 10 * ngs.sin(ngs.x) * ngs.sin(ngs.y)
op = Coefficient(domain,
rhs,
codomain=codomain,
bc_left=0,
bc_right=0,
bc_bottom=0,
bc_top=0,
diffusion=False,
reaction=True,
dim=2)
exact_solution_coeff = ngs.x + 1
gfu_exact_solution = ngs.GridFunction(op.fes_domain)
gfu_exact_solution.Set(exact_solution_coeff)
exact_solution = gfu_exact_solution.vec.FV().NumPy()
exact_data = op(exact_solution)
fes_noise = ngs.L2(fes_codomain.mesh, order=1)
gfu_noise_order1 = ngs.GridFunction(fes_noise)
gfu_noise_order1.vec.FV().NumPy()[:] = 0.0001 * np.random.randn(fes_noise.ndof)
gfu_noise = ngs.GridFunction(fes_codomain)
gfu_noise.Set(gfu_noise_order1)
noise = gfu_noise.vec.FV().NumPy()
data = exact_data + noise
init = 1 + ngs.x**2
init_gfu = ngs.GridFunction(op.fes_domain)
#pc_opts = { "ngs_amg_reg_rmats" : True }
pc_opts = {
"ngs_amg_reg_rmats": True,
"ngs_amg_rots": False,
"mgs_amg_max_levels": 2,
#"ngs_amg_aaf" : 0.25,
"ngs_amg_max_coarse_size": 20,
#"ngs_amg_max_levels" : 4,
"ngs_amg_log_level": "extra",
"ngs_amg_enable_sp": True,
"ngs_amg_sp_max_per_row": 4,
"ngs_amg_enable_redist": True,
"ngs_amg_first_aaf": 0.025
}
gfu = ngsolve.GridFunction(V)
a.Assemble()
f.Assemble()
gfu.vec.data = a.mat.Inverse(V.FreeDofs()) * f.vec
#ngsolve.Draw(mesh, deformation = ngsolve.CoefficientFunction((gfu[0], gfu[1], gfu[2])), name="defo")
ngsolve.Draw(mesh,
deformation=ngsolve.CoefficientFunction((gfu[0], gfu[1])),
name="defo")
ngsolve.Draw(gfu[2], mesh, name="rot")
# for i in range(6):
# ngsolve.Draw(gfu[i], mesh, name="comp_"+str(i))
# ngsolve.Draw(gfu, name="sol")
# # c = ngsolve.Preconditioner(a, "ngs_amg.elast3d", **pc_opts)
def solve(self):
# disable garbage collector
# --------------------------------------------------------------------#
gc.disable()
while (gc.isenabled()):
time.sleep(0.1)
# --------------------------------------------------------------------#
# measure how much memory is used until here
process = psutil.Process()
memstart = process.memory_info().vms
# starts timer
tstart = time.time()
if self.show_gui:
import netgen.gui
# create mesh with initial size 0.1
self._mesh = ngs.Mesh(unit_square.GenerateMesh(maxh=0.1))
#create finite element space
self._fes = ngs.H1(self._mesh,
order=2,
dirichlet=".*",
autoupdate=True)
# test and trail function
u = self._fes.TrialFunction()
v = self._fes.TestFunction()
# create bilinear form and enable static condensation
self._a = ngs.BilinearForm(self._fes, condense=True)
self._a += ngs.grad(u) * ngs.grad(v) * ngs.dx
# creat linear functional and apply RHS
self._f = ngs.LinearForm(self._fes)
self._f += (-4) * v * ngs.dx
# preconditioner: multigrid - what prerequisits must the problem have?
self._c = ngs.Preconditioner(self._a, "multigrid")
# create grid function that holds the solution and set the boundary to 0
self._gfu = ngs.GridFunction(self._fes, autoupdate=True) # solution
self._g = self._ngs_ex
self._gfu.Set(self._g, definedon=self._mesh.Boundaries(".*"))
# draw grid function in gui
if self.show_gui:
ngs.Draw(self._gfu)
# create Hcurl space for flux calculation and estimate error
self._space_flux = ngs.HDiv(self._mesh, order=2, autoupdate=True)
self._gf_flux = ngs.GridFunction(self._space_flux,
"flux",
autoupdate=True)
# TaskManager starts threads that (standard thread nr is numer of cores)
with ngs.TaskManager():
# this is the adaptive loop
while self._fes.ndof < self.max_ndof:
self._solveStep()
self._estimateError()
self._mesh.Refine()
# since the adaptive loop stopped with a mesh refinement, the gfu must be
# calculated one last time
self._solveStep()
if self.show_gui:
ngs.Draw(self._gfu)
# set measured exectution time
self._exec_time = time.time() - tstart
# set measured used memory
memstop = process.memory_info().vms - memstart
self._mem_consumption = memstop
# enable garbage collector
# --------------------------------------------------------------------#
gc.enable()
gc.collect()
def _copy_data(self):
new_impl = ngs.GridFunction(self.impl.space)
new_impl.vec.data = self.impl.vec
self.impl = new_impl
def __init__(self, domain, g, codomain=None):
codomain = codomain or domain
self.g = g
# self.pts=pts
# Define mesh and finite element space
# geo=SplineGeometry()
# geo.AddCircle((0,0), 1, bc="circle")
# ngmesh = geo.GenerateMesh()
# ngmesh.Save('ngmesh')
# self.mesh=MakeQuadMesh(10)
# self.mesh=Mesh(ngmesh)
self.fes_domain = domain.fes
self.fes_codomain = codomain.fes
# Variables for setting of boundary values later
# self.ind=[v.point in pts for v in self.mesh.vertices]
self.pts = [v.point for v in self.fes_codomain.mesh.vertices]
self.ind = [np.linalg.norm(np.array(p)) > 0.95 for p in self.pts]
self.pts_bdr = np.array(self.pts)[self.ind]
self.fes_in = ngs.H1(self.fes_codomain.mesh, order=1)
self.gfu_in = ngs.GridFunction(self.fes_in)
# grid functions for later use
self.gfu = ngs.GridFunction(
self.fes_codomain) # solution, return value of _eval
self.gfu_bdr = ngs.GridFunction(
self.fes_codomain
) # grid function holding boundary values, g/sigma=du/dn
self.gfu_integrator = ngs.GridFunction(
self.fes_domain
) # grid function for defining integrator (bilinearform)
self.gfu_integrator_codomain = ngs.GridFunction(self.fes_codomain)
self.gfu_rhs = ngs.GridFunction(
self.fes_codomain
) # grid function for defining right hand side (linearform), f
self.gfu_inner_domain = ngs.GridFunction(
self.fes_domain
) # grid function for reading in values in derivative
self.gfu_inner = ngs.GridFunction(
self.fes_codomain
) # grid function for inner computation in derivative and adjoint
self.gfu_deriv = ngs.GridFunction(
self.fes_codomain) # gridd function return value of derivative
self.gfu_toret = ngs.GridFunction(
self.fes_domain
) # grid function for returning values in adjoint and derivative
self.gfu_dir = ngs.GridFunction(
self.fes_domain
) # grid function for solving the dirichlet problem in adjoint
self.gfu_error = ngs.GridFunction(
self.fes_codomain
) # grid function used in _target to compute the error in forward computation
self.gfu_tar = ngs.GridFunction(
self.fes_codomain
) # grid function used in _target, holding the arguments
self.gfu_adjtoret = ngs.GridFunction(self.fes_domain)
self.Number = ngs.NumberSpace(self.fes_codomain.mesh)
r, s = self.Number.TnT()
u = self.fes_codomain.TrialFunction() # symbolic object
v = self.fes_codomain.TestFunction() # symbolic object
# Define Bilinearform, will be assembled later
self.a = ngs.BilinearForm(self.fes_codomain, symmetric=True)
self.a += ngs.SymbolicBFI(
ngs.grad(u) * ngs.grad(v) * self.gfu_integrator_codomain)
########new
self.a += ngs.SymbolicBFI(
u * s + v * r, definedon=self.fes_codomain.mesh.Boundaries("cyc"))
self.fes1 = ngs.H1(self.fes_codomain.mesh,
order=2,
definedon=self.fes_codomain.mesh.Boundaries("cyc"))
self.gfu_getbdr = ngs.GridFunction(self.fes1)
self.gfu_setbdr = ngs.GridFunction(self.fes_codomain)
# Define Linearform, will be assembled later
self.f = ngs.LinearForm(self.fes_codomain)
self.f += ngs.SymbolicLFI(self.gfu_rhs * v)
self.r = self.f.vec.CreateVector()
self.b = ngs.LinearForm(self.fes_codomain)
self.gfu_b = ngs.GridFunction(self.fes_codomain)
self.b += ngs.SymbolicLFI(
self.gfu_b * v.Trace(),
definedon=self.fes_codomain.mesh.Boundaries("cyc"))
self.f_deriv = ngs.LinearForm(self.fes_codomain)
self.f_deriv += ngs.SymbolicLFI(self.gfu_rhs * ngs.grad(self.gfu) *
ngs.grad(v))
# self.b2=LinearForm(self.fes)
# self.b2+=SymbolicLFI(div(v*grad(self.gfu))
super().__init__(domain, codomain)
def __init__(self, domain, g, codomain=None):
codomain = codomain or domain
self.g = g
self.fes_domain = domain.fes
self.fes_codomain = codomain.fes
self.fes_in = ngs.H1(self.fes_codomain.mesh, order=1)
self.gfu_in = ngs.GridFunction(self.fes_in)
# grid functions for later use
self.gfu = ngs.GridFunction(
self.fes_codomain) # solution, return value of _eval
# self.gfu_bdr=ngs.GridFunction(self.fes_codomain) #grid function holding boundary values, g/sigma=du/dn
self.gfu_bilinearform = ngs.GridFunction(
self.fes_domain
) # grid function for defining integrator (bilinearform)
self.gfu_bilinearform_codomain = ngs.GridFunction(
self.fes_codomain
) # grid function for defining integrator of bilinearform
self.gfu_linearform_domain = ngs.GridFunction(
self.fes_codomain) # grid function for defining linearform
self.gfu_linearform_codomain = ngs.GridFunction(self.fes_domain)
self.gfu_deriv_toret = ngs.GridFunction(
self.fes_codomain) # grid function: return value of derivative
self.gfu_adj = ngs.GridFunction(
self.fes_domain) # grid function for inner computation in adjoint
self.gfu_adj_toret = ngs.GridFunction(
self.fes_domain) # grid function: return value of adjoint
self.gfu_b = ngs.GridFunction(
self.fes_codomain) # grid function for defining the boundary term
u = self.fes_codomain.TrialFunction() # symbolic object
v = self.fes_codomain.TestFunction() # symbolic object
# Define Bilinearform, will be assembled later
self.a = ngs.BilinearForm(self.fes_codomain, symmetric=True)
self.a += ngs.SymbolicBFI(-ngs.grad(u) * ngs.grad(v) +
u * v * self.gfu_bilinearform_codomain)
# Interaction with Trace
self.fes_bdr = ngs.H1(
self.fes_codomain.mesh,
order=self.fes_codomain.globalorder,
definedon=self.fes_codomain.mesh.Boundaries("cyc"))
self.gfu_getbdr = ngs.GridFunction(self.fes_bdr)
self.gfu_setbdr = ngs.GridFunction(self.fes_codomain)
# Boundary term
self.b = ngs.LinearForm(self.fes_codomain)
self.b += ngs.SymbolicLFI(
-self.gfu_b * v.Trace(),
definedon=self.fes_codomain.mesh.Boundaries("cyc"))
# Linearform (only appears in derivative)
self.f_deriv = ngs.LinearForm(self.fes_codomain)
self.f_deriv += ngs.SymbolicLFI(-self.gfu_linearform_codomain *
self.gfu * v)
super().__init__(domain, codomain)
def real_zero_vector(self):
impl = ngs.GridFunction(self.V)
return NGSolveVector(impl)
def __init__(self,
domain,
rhs,
bc_left=None,
bc_right=None,
bc_top=None,
bc_bottom=None,
codomain=None,
diffusion=True,
reaction=False,
dim=1):
assert dim in (1, 2)
assert diffusion or reaction
codomain = codomain or domain
self.rhs = rhs
self.diffusion = diffusion
self.reaction = reaction
self.dim = domain.fes.mesh.dim
bc_left = bc_left or 0
bc_right = bc_right or 0
bc_top = bc_top or 0
bc_bottom = bc_bottom or 0
# Define mesh and finite element space
self.fes_domain = domain.fes
# self.mesh=self.fes.mesh
self.fes_codomain = codomain.fes
# if dim==1:
# self.mesh = Make1DMesh(meshsize)
# self.fes = H1(self.mesh, order=2, dirichlet="left|right")
# elif dim==2:
# self.mesh = MakeQuadMesh(meshsize)
# self.fes = H1(self.mesh, order=2, dirichlet="left|top|right|bottom")
# grid functions for later use
self.gfu = ngs.GridFunction(
self.fes_codomain) # solution, return value of _eval
self.gfu_bdr = ngs.GridFunction(
self.fes_codomain) # grid function holding boundary values
self.gfu_integrator = ngs.GridFunction(
self.fes_domain
) # grid function for defining integrator (bilinearform)
self.gfu_integrator_codomain = ngs.GridFunction(self.fes_codomain)
self.gfu_rhs = ngs.GridFunction(
self.fes_codomain
) # grid function for defining right hand side (Linearform)
self.gfu_inner_domain = ngs.GridFunction(
self.fes_domain
) # grid function for reading in values in derivative
self.gfu_inner = ngs.GridFunction(
self.fes_codomain
) # grid function for inner computation in derivative and adjoint
self.gfu_deriv = ngs.GridFunction(
self.fes_codomain) # return value of derivative
self.gfu_toret = ngs.GridFunction(
self.fes_domain
) # grid function for returning values in adjoint and derivative
u = self.fes_codomain.TrialFunction() # symbolic object
v = self.fes_codomain.TestFunction() # symbolic object
# Define Bilinearform, will be assembled later
self.a = ngs.BilinearForm(self.fes_codomain, symmetric=True)
if self.diffusion:
self.a += ngs.SymbolicBFI(
ngs.grad(u) * ngs.grad(v) * self.gfu_integrator_codomain)
elif self.reaction:
self.a += ngs.SymbolicBFI(
ngs.grad(u) * ngs.grad(v) +
u * v * self.gfu_integrator_codomain)
# Define Linearform, will be assembled later
self.f = ngs.LinearForm(self.fes_codomain)
self.f += ngs.SymbolicLFI(self.gfu_rhs * v)
if diffusion:
self.f_deriv = ngs.LinearForm(self.fes_codomain)
self.f_deriv += ngs.SymbolicLFI(-self.gfu_rhs *
ngs.grad(self.gfu) * ngs.grad(v))
# Precompute Boundary values and boundary valued corrected rhs
if self.dim == 1:
self.gfu_bdr.Set(
[bc_left, bc_right],
definedon=self.fes_codomain.mesh.Boundaries("left|right"))
elif self.dim == 2:
self.gfu_bdr.Set([bc_left, bc_top, bc_right, bc_bottom],
definedon=self.fes_codomain.mesh.Boundaries(
"left|top|right|bottom"))
self.r = self.f.vec.CreateVector()
super().__init__(domain, codomain)